How do I properly normalize a function over a region in space?

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SUMMARY

The discussion focuses on the normalization of the function Q = ∫(1 - y²) dx dy. The user attempted to normalize this function using the expression |N|² |∫Q*Q dx dy|² = 1, leading to the result N = 1 / (x(y - y³/3)). However, the normalization equation was incorrectly stated, and the evaluation of the double integral was flawed. The consensus is that the normalization factor should solely depend on the boundaries of the region being examined, necessitating a reevaluation of both the function Q and the normalization process.

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  • Familiarity with normalization in quantum mechanics
  • Knowledge of complex conjugates and their role in integrals
  • Basic principles of function evaluation over defined regions
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germana2006
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Homework Statement



I have normalized the following function:

[tex]Q=\int (1-y^2) dx dy[/tex]

Homework Equations



using the expression for the normalization

[tex]\vert N \vert ^2 \vert \int Q^* Q dx dy \vert^2 =1[/tex]


The Attempt at a Solution



then I obtained

[tex]\int Q^* Q dx dy = x (y- y^3 /3)[/tex]

therefore

[tex]N = 1/ x (y- y^3 /3)[/tex]

but I am not sure if I have done good.
 
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You normalize functions over regions in space. The normalization factor should not be a function of anything but perhaps the boundary of the region you're examining.

And you either stated your function Q incorrectly or you evaluated the double integral incorrectly. Also you stated your normalization equation wrong, you're doubling up on the squaring.

You need to start over from the beginning.
 

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